A skein relation is a set of rules defining a knot polynomial invariant with givens and associations between crossings. For example, the skein relation for the Jones Polynomial is
Rule 1: VU(t) = 1
Rule 2: t-1 · VL+(t) - t · VL-(t) = (t1/2 - t-1/2) · VL0(t)
Where VU(t) represents the Jones Polynomial of the unknot, and VL+(t), VL-(t), and VL0(t) represent the Jones Polynomials of the same knot if a selected crossing was of type L+, L-, or L0 as shown below.
A crossing in a knot diagram is selected as the first step in using a skein relation. Then, the type of crossing is determined and the polynomial is solved for that type of crossing. For instance, if a crossing of type L+ was selected in calculating the Jones Polynomial, the equation is solved for VL+(t). Then a new knot diagram is drawn for each of the other crossing types. In the case just mentioned, two new diagrams are drawn with crossings of type L- and L0 instead of L+, and the polynomial invariants of those diagrams are calculated. If the polynomial invariant is an isotopy invariant, the diagrams can be simplified using the Reidemeister Moves before continuing. If not, like the Bracket Polynomial, the invariant must be calculated without simplification.